Numbers Needed to Treat

Risk Reductions and the Number Needed to Treat-Rational Decisions between Interventions

Simulated Clinical Scenario

Dr X is working at a community health center that has a running battle with diarrhea in children aged 1-4 years. The initial line of management for the less severe cases is packs of oral rehydration solution at presentation to the OP.  Usually, 20% of these children (with less severe diarrhea at presentation) come back requiring an IV infusion.  Your team believes the IV infusion rate could be much less if parents were compliant with the recommended administration of ORS to children.

A colleague working in another CHC nearby informs your team that they use (a CHC in a similar geo-demographic setting) a newer antibiotic that administered as a single intramuscular injection . He said 15% of children who were administered the intramuscular injection required subsequent IV infusions but there was more compliance than with ORS and that the injections were more convenient.

Dr X is not sure whether to start the newer antibiotics or not.

Please help Dr X reach a reasoned decision.

 

Points to consider

  1. Determine the outcome event of interest- Subsequent IV infusion
  2. What do we want to see-Is there a reduction in the risk for subsequent IV infusion if we give the injections?
  3. What is the control group- Group that receives ORS
  4. What is the intervention group- Group that receives the newer antibiotic
  5. What is the control group event rate- Number of IV infusions in those who receive ORS
  6. What is the intervention group event rate- Number of IV infusions

How do we use these?

  1. What is the absolute risk of subsequent IV infusions in the control group- 20%
  2. What is the absolute risk of subsequent IV infusions in the intervention group-15%
  3. What is the difference in the risk for subsequent IV infusions in the two groups? This is the absolute risk reduction (ARR) or difference between the control and intervention event rates. This is estimated as the control event rate-intervention event rate (because we will be interested in the intervention only if the rates are lower in the intervention group).
  4. In this case, the absolute risk reduction is 20%-15% = 5% or 0.05
  5. So we see there is a 5% reduction in subsequent IV infusions if we give the injections.
  6. We could check the reduction in risk with the newer antibiotic compared with or relative to the ORS. This is the relative risk reduction (RRR). Compared to ORS, how much does the newer antibiotic reduce the risk for subsequent IV infusions?
  7. We can estimate the relative risk reduction as the (control group event-intervention group event)/ control group event.
  8. In this case, the relative risk reduction is (20%-15%)/20%= (0.20-0.15)/0.20= 0.05/0.20=0.25 or 25%
  9. We now see that the absolute risk reduction is 5% but the relative risk reduction is 25%

Dr X says “All this science and maths is good, but I just want to know what will happen if I change to administering the injections.  How do I use the percentages to decide?”

Let us look at the number needed to treat or NNT.

The number needed to treat is the number of patients you need to treat to expect to prevent one additional bad outcome.

The NNT= 1/ARR= 1/0.05=20

What does this mean?

It means that Dr X can expect to prevent one subsequent IV infusion for every 20 children administered the injection.  If 100 children are administered the injection, Dr X may have prevented the need for a subsequent IV infusion in 5 children. 

Dr X now looks at his data and says, “Well, 20 of 100 children that I give ORS to require subsequent IV infusions.  If I give the injections, 15 of 100 children may need subsequent IV infusions but I can prevent the need for subsequent IV infusions in 5 of 100 children.  My OP runs to about 500 children a month with diarrhea, so I would have prevented subsequent IV infusions in 25 children each month”

Dr X then considers the potential complication rate, cost, availability, etc of the injection and weighs that against the benefits of preventing 5 IV infusions to make a decision.

NOTE: LOOK AT THE CONFIDENCE INTERVALS AROUND THE NNT TO MAKE A DECISION (WE HAVE NOT COVERED THAT HERE).